The corresponding time-dependent wave function \(|\psi ^{(1)}(t)\rangle \equiv \sum _{J^{\prime }=0}^2c_{J^{\prime }}^{(1)}|J^{\prime }0\rangle =\hat{U}^{(1)}(t, t_0)|00\rangle \)  starting from the ground rotational state \(|00\rangle \)  can be given by [1]}
\( |\psi ^{(1)}(t)\rangle &=&\frac{[\left|\theta _2(t)\right|^2+\left|\theta _1(t)\right|^2\cos \theta _{12}(t)]}{\theta _{12}^2(t)}|00\big \rangle \\ \ \nonumber &&+\frac{i\theta _1(t)\sin \theta _{12}(t)}{\theta _{12}(t)}|10\rangle +\frac{\theta _1(t)\theta _2(t)}{\theta _{12}^2(t)}\left[\cos \theta _{12}(t)-1\right]|20\rangle ,\) 
